A Result on K-(2,1)-Total Choosability of Planar Graphs  

作　　者：Yan SONG Lei SUN 

机构地区：[1]Department of Mathematics,Shandong Normal University,Shandong 250014,P.R China

出　　处：《Journal of Mathematical Research with Applications》2022年第2期121-128,共8页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12071265);the Natural Science Foundation of Shandong Province(Grant No.ZR2019MA032)。

摘　　要：A list assignment of a graph G is a function L:V(G)∪E(G)→2^(N).A graph G is L-(2,1)-Total labeling if there exists a function c such that c(x)∈L(x)for all x∈V(G)∪E(G),|c(u)-c(v)|≥1 if uv∈E(G),|c(e_(1))-c(e_(2))|≥1 if the edges e_(1)and e_(2)are adjacent,and|c(u)-c(e)|≥2 if the vertex u is incident to the edge e.A graph G is k-(2,1)-Total choosable if G is L-(2,1)-Total labeling for every list assignment L provided that|L(x)|=k,x∈V(G)∪E(G).The(2,1)-Total choice number of G,denoted by C_(2,1)^T(G),is the minimum k such that G is k-(2,1)-Total choosable.In this paper,we prove that if G is a planar graph with△(G)≥11,then C_(2,1)^T(G)≤△+4.

关 键 词：L-(2 1)-total labeling k-(2 1)-total choosable planar graphs 

分 类 号：O157.5[理学—数学]